The present invention relates generally to process control systems and, more particularly, to model predictive control of one or more asymmetrical process parameters in a process.
Manufacturing processes typically share the common goal of ensuring that a resulting product conforms to certain target quality specifications. In controlling a process in this regard, a determination as to whether a resulting product conforms to a particular quality standard may be indicated by one or more quality parameters derived or measured during the process. In some instances, these quality parameters may be measured online by using one or more measurement devices, such as sensors, transducers, or the like. Thus, using measured quality parameter values, a control system may be able to adjust one or more process variables of the manufacturing process in order to maintain the quality parameter at a desired target value (e.g., a set point, range, or maximum, etc.).
In some processes, certain quality parameters may not be directly measurable using conventional sensors and measuring devices. For example, in a paper manufacturing process, certain quality parameters of a finished paper product, such as a paper strength property, are typically only measurable by taking a sample of finished paper and performing various destructive tests in a testing setting that is separate from the process, such as in a dedicated or automated testing system, through one or more laboratory-based tests or measurements, or by other offline product testing arrangements (e.g., including offline sensors not in direct communication with the process system). These samples are normally taken when a reel of finished paper is removed from the paper machine. Thus, these “off-process” measurements may not be available for use in the process for control purposes during the production of the reel from which the measurement is obtained.
One solution for providing closed loop control of a parameter that cannot be directly measured while a process is running is through the use of one or more inferential models configured to provide a predicted value of the parameter. The predicted values which may be used by a dynamic predictive control model to control one or more manipulated variables (MV's) of the process in order to drive the predicted values produced by the inferential model towards a desired target set point or range of acceptable values. Generally, the inferential model differentially determines a predicted or estimated value for the parameter based upon relationships between one or more MV's and/or disturbance variables (DV's) of the process. As will be appreciated, MV's are those variables which can be controlled by a controller in order to achieve the targets or goals indicated by controlled variables (CV's) which the controller tries to bring to some objective (e.g., to a target set point, maximum, etc.). DV's may be regarded as those variables which may affect the resulting objective parameter (e.g., paper quality parameter), but that the controller may not be able to regulate.
While the use of inferential models in measuring such parameters provides a baseline for closed loop control, mismatches between the predicted value and an actual value of the parameter (e.g., laboratory measurement) may occur due to imperfections in the modeling algorithms, unmeasured disturbances and, in some cases, immeasurable disturbances in the process system. Accordingly, a prediction error may be determined by comparing the predicted value of the parameter with a corresponding off-process measurement taken from a sample of a finished product. This prediction error may be used to compute a biasing factor that is used to bias the predicted values provided by the inferential model, thus producing an adjusted predicted value of the quality parameter which may be used by a dynamic predictive control model to determine the appropriate control actions required for driving the parameter towards the target set point. However, the use of the off-process measurements themselves is not without drawbacks. For example, in many cases, off-process measurements have their own disturbance characteristics due to inconsistencies or human/machine errors in performing or obtaining measurements. Often times, measurements taken from multiple samples obtained from the same sheet of paper may produce different measurements. Thus, off-process measurements are often filtered such that a biasing factor used in adjusting the predicted values from the inferential model may only reflect a portion of the prediction error.
Still further, certain processes parameters may have asymmetrical characteristics with a limit imposed more strictly in one direction than the opposing direction. For example, in the case of a paper strength parameter, an asymmetrical characteristic may be that the paper product must at least meet a certain strength value. If the paper fails to meet at least the target strength value, the paper may be rejected as being unmarketable, thus resulting in a loss of return on all operation costs associated with producing the rejected product. However, if the paper exceeds the specified strength value, this deviation may be acceptable, though not necessarily optimal in terms of production costs, for example. That is, the marginal cost of producing a product that exceeds a target specification is often preferable to producing a rejected product that fails to even satisfy the minimum acceptable specifications. Accordingly, there exists a need for a technique to adaptively control an asymmetrical process parameter based on laboratory measurements to correct for prediction mismatches more quickly in a particular direction.